Top Student: Wasteland Technology Invasion

"Time has the properties of quantum mechanics. The time you have experienced has collapsed into a single instant. The time you have not experienced is still in a wave state before it is observed by anyone."

Lin Chuan came to understand the meaning of this passage while learning mathematics in the wasteland world.

Even without unlocking any skills, the time it took for him to gain 2 experience points in mathematics was truly just a fleeting moment.

Mathematics: Level 2 (200/400)

[Reward: Improved efficiency in learning fundamental mathematics]

[Reward: Improved basic mathematical understanding]

[Reward: 200 Learning Coins]

[Reward: Increases carrying capacity by 5kg when traversing the wasteland world]

[Reward: Daily travel time increased by 1 hour]

[Reward: Unlocks the ability to create anchor points]

"This is……"

It's been upgraded!

Lin Chuan felt a surge of joy; all his hard work traversing between the two worlds to gain experience over the past few days had finally paid off.

"Learning efficiency and comprehension ability are a bit abstract; we'll look at them later."

"200 learning coins, great stuff!"

"Transmigrating to a wasteland world increases my carrying capacity by 5kg..."

"Doubling the carrying capacity allows me to bring a lot of stuff into the wasteland; I can even try moving the generators over separately."

Unfortunately, it's still impossible to move things into the real world...

"Increasing the traversal time by one hour is a tangible benefit, and the added weight capacity has increased to 10kg. Even if the traversal time is rounded down to the hour, if I go twice a day, morning and evening, I can carry 20kg of supplies."

"So, that means our carrying capacity has quadrupled!"

"And then there's this initial anchor point."

After careful study, Lin Chuan understood how to use the ability to open up anchor points.

He can now open a second travel anchor point in the wasteland world by spending only 100 learning coins.

Currently, the maximum number of anchor points in the Wasteland world is two.

Besides its normal use for traversing between worlds, anchor points have gained a new purpose.

He can spend 10 study coins at any time to travel between two anchor points in the wasteland.

This undoubtedly greatly enhanced his safety in the wasteland.

At the same time, he can spend 10 learning coins to move the existing anchor point within a certain range. As for the exact range, Lin Chuan does not plan to leave the safe house to explore, so he has not tried it yet.

……

When he returned to the real world, it was almost lunchtime. Instead of going to the cafeteria, Lin Chuan went to the library to get his computer.

He planned to test his improved math skills before copying the last part of the paper onto the computer.

Lin Chuan took out his textbook, "Algebraic Geometry," a course typically taught to third-year university students, and had tried looking at it a few times.

However, given the scarcity of learning coins and the inability to unlock skills, he had only skimmed through the first chapter. Now, he could use it to test the effectiveness of his improved learning efficiency and comprehension.

"Let k be an algebraically closed field. Consider the set of affine algebras V = V(xy−1) in the affine space Ak^2, where xy−1∈k[x,y] is a polynomial."

Describe the geometry of V and prove that V is irreducible. Find the coordinate ring k[V] of V and describe its structure.

This is a very ordinary quiz question from the first chapter of "Algebraic Geometry".

If it were before he went to the wasteland this morning, Lin Chuan might have been too tired to answer.

But now, he quickly flipped through the first chapter of "Algebraic Geometry" and began learning on the spot.

[Learning Coin +1]

[Learning Coin +1]

[Your hard work has earned you +1 math experience]

Mathematics: Level 2 (201/400)

My mathematical experience has increased!

Compared to his previous learning speed in the real world, Lin Chuan felt that his learning efficiency had improved by at least 30% this time.

Quite a considerable gain!

The learning session is over; let's start answering the questions.

The first question...

'V = {(x, y) ∈ Ak^2 | xy = 1} is a hyperbola in Ak^2, which represents a smooth curve in the complex plane when k = C.'

"Irreducibility means that V cannot be represented as the union of two proper algebraic subsets; equivalently, it needs to be proven that the ideal I(V) is a prime ideal of k[x, y]."

Since k is an algebraically closed field, I(V) = (xy−1), and xy−1 is an irreducible polynomial, so (xy−1) is a prime ideal, and therefore I(V) = (xy−1).

'The algebraic set corresponding to a prime ideal is irreducible, therefore V is irreducible.'

Question 2...

The coordinate loop is defined as k[V] = k[x, y] / I(V) = k[x, y] / (xy−1).

In the quotient ring, the relation xy=1 means that y is the multiplicative inverse of x, i.e., y=x^−1.

Therefore, k[V] ≅ k[x, x^−1].

Lin Chuan arrived at the answer.

The whole process was exhilarating and seamless.

Although Lin Chuan was far from reaching the level of having activated the skill "Scientific Intuition" in the wasteland world during this problem-solving process, it was still much better than his previous self-exploration and learning in the real world.

"So clear."

Although it was just a simple quiz question in Algebraic Geometry, Lin Chuan felt a sense of exhilaration at glimpsing the truth after solving it.

"Is this what it feels like to upgrade your math skills and improve your comprehension?"

"handy!"

"Next, I'll work on the paper, then go eat!"

……

At Viet Yang University, many professors proactively recommend important books needed for the development of their departments and disciplines to the library, helping to enrich the library's collection. Some scholars even donate their own professional collections to the library.

Professor Lu Zhiwei had just donated his collection of books and was walking out when he caught a glimpse of a young man engrossed in studying something.

Lin Chuan was so focused that Professor Lu was immediately drawn in by his state of mind.

"Algebraic Geometry, are you a third-year math major? You look quite young."

Soon, Lu Zhiwei realized something was wrong.

The arithmetic symbols on this young man's draft paper are a bit exaggerated.

And it seems he's writing a thesis.

Lu Zhiwei took a few steps closer and glimpsed that Lin Chuan's draft paper initially contained content related to special non-self-adjoint matrices from "Higher Algebra," followed by a section on "Functional Analysis."

As Professor Lu continued reading, he couldn't quite understand it anymore.

The handwriting on Chun Chuan's draft paper was really messy.

"This is……"

Professor Lu turned his gaze to Lin Chuan's laptop, where he saw the following text: "Research Summary: The article clarifies the fundamental differences between non-self-adjoint matrices and self-adjoint matrices in their spectral properties. The eigenvalues ​​of non-self-adjoint matrices may be complex, and their eigenvector systems are not necessarily orthogonal or complete..."

Upon seeing this, Professor Lu raised an eyebrow.

"This is unusual."

"This young man is a junior in college. Even in the Qiushi Class, his level is outstanding."

"That's strange. Does the Department of Mathematics have such a student? I don't recognize him!"

At this moment, Lin Chuan was completely immersed in the world of academic papers. During his "seclusion" in the wasteland world for the past few days, he had been studying mathematics every day.

This paper is a manifestation of the research findings.

In this state of deep concentration, Lin Chuan was naturally unaware that a professor had appeared beside him.

Moreover, he not only failed to notice the professor, he also failed to notice whether he was hungry.

at last.

Lin Chuan typed the last line of his paper, leaned back in his chair, and let out a long sigh.

"I'm quite tired."

"But studying mathematics so intently without using any special skills feels pretty good."

Lin Chuan scrolled through his paper with a sense of accomplishment as he finished preparing it for submission.

Suddenly, a pair of large hands patted his shoulder and whispered, "Excuse me, what's your name?"

Lin Chuan was startled and turned around abruptly. He saw a middle-aged man, who looked to be in his forties or fifties and whose hairline was receding, greeting him with a smile.